The Turkish international left-back has been in impressive for the Black Eagles establishing himself as a first-team regular for the Turkish Super League leaders.
Koybaşı has provided one assist in 18 appearances in all competitions for Beşiktaş this season but has just six-months remaining on his contract.
The 26-year-old full-back has yet to agree a new deal with the Istanbul giants and the likes of Liverpool and Valencia would be able to sign him on a free contract at the end of the season.
Koybaşı is expected to travel with the Turkish national team to the European Championships in France over the summer and has 15 international caps.
The Eagles left-back has been one of the best performing defensive players in the team this season averaging 2.2 tackles and 2.8 interceptions per-game. Koybaşı also uses his pace well to burst forward into forward positions – averaging 1.3 successful dribbles per-game – and has good crossing ability.